Integrand size = 275, antiderivative size = 34 \[ \int \frac {e^{12} \left (128-320 x+352 x^2-240 x^3+120 x^4-44 x^5+10 x^6-x^7\right )+e^{\frac {1+4 e^3 x+e^6 \left (-8 x+14 x^2-2 x^3\right )+e^9 \left (-16 x^2+20 x^3-4 x^4\right )+e^{12} \left (16 x^2-40 x^3+33 x^4-10 x^5+x^6\right )}{e^{12} \left (16-32 x+24 x^2-8 x^3+x^4\right )}} \left (-4 x+e^3 \left (-8 x-12 x^2\right )+e^6 \left (16 x-32 x^2-16 x^3+2 x^4\right )+e^9 \left (64 x^2-88 x^3+12 x^4\right )+e^{12} \left (32-80 x+16 x^2+168 x^3-214 x^4+99 x^5-22 x^6+2 x^7\right )\right )}{e^{12} \left (-32 x^2+80 x^3-80 x^4+40 x^5-10 x^6+x^7\right )} \, dx=\frac {4+e^{\left (x-\frac {\left (\frac {1}{e^3}+x\right )^2}{(-2+x)^2}\right )^2}-2 x-x^2}{x} \] Output:
(exp((x-(exp(-3)+x)^2/(-2+x)^2)^2)+4-x^2-2*x)/x
Time = 0.34 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.35 \[ \int \frac {e^{12} \left (128-320 x+352 x^2-240 x^3+120 x^4-44 x^5+10 x^6-x^7\right )+e^{\frac {1+4 e^3 x+e^6 \left (-8 x+14 x^2-2 x^3\right )+e^9 \left (-16 x^2+20 x^3-4 x^4\right )+e^{12} \left (16 x^2-40 x^3+33 x^4-10 x^5+x^6\right )}{e^{12} \left (16-32 x+24 x^2-8 x^3+x^4\right )}} \left (-4 x+e^3 \left (-8 x-12 x^2\right )+e^6 \left (16 x-32 x^2-16 x^3+2 x^4\right )+e^9 \left (64 x^2-88 x^3+12 x^4\right )+e^{12} \left (32-80 x+16 x^2+168 x^3-214 x^4+99 x^5-22 x^6+2 x^7\right )\right )}{e^{12} \left (-32 x^2+80 x^3-80 x^4+40 x^5-10 x^6+x^7\right )} \, dx=\frac {4+e^{\frac {\left (1+2 e^3 x-e^6 x \left (4-5 x+x^2\right )\right )^2}{e^{12} (-2+x)^4}}-x^2}{x} \] Input:
Integrate[(E^12*(128 - 320*x + 352*x^2 - 240*x^3 + 120*x^4 - 44*x^5 + 10*x ^6 - x^7) + E^((1 + 4*E^3*x + E^6*(-8*x + 14*x^2 - 2*x^3) + E^9*(-16*x^2 + 20*x^3 - 4*x^4) + E^12*(16*x^2 - 40*x^3 + 33*x^4 - 10*x^5 + x^6))/(E^12*( 16 - 32*x + 24*x^2 - 8*x^3 + x^4)))*(-4*x + E^3*(-8*x - 12*x^2) + E^6*(16* x - 32*x^2 - 16*x^3 + 2*x^4) + E^9*(64*x^2 - 88*x^3 + 12*x^4) + E^12*(32 - 80*x + 16*x^2 + 168*x^3 - 214*x^4 + 99*x^5 - 22*x^6 + 2*x^7)))/(E^12*(-32 *x^2 + 80*x^3 - 80*x^4 + 40*x^5 - 10*x^6 + x^7)),x]
Output:
(4 + E^((1 + 2*E^3*x - E^6*x*(4 - 5*x + x^2))^2/(E^12*(-2 + x)^4)) - x^2)/ x
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {\left (e^3 \left (-12 x^2-8 x\right )+e^6 \left (2 x^4-16 x^3-32 x^2+16 x\right )+e^9 \left (12 x^4-88 x^3+64 x^2\right )+e^{12} \left (2 x^7-22 x^6+99 x^5-214 x^4+168 x^3+16 x^2-80 x+32\right )-4 x\right ) \exp \left (\frac {e^6 \left (-2 x^3+14 x^2-8 x\right )+e^9 \left (-4 x^4+20 x^3-16 x^2\right )+e^{12} \left (x^6-10 x^5+33 x^4-40 x^3+16 x^2\right )+4 e^3 x+1}{e^{12} \left (x^4-8 x^3+24 x^2-32 x+16\right )}\right )+e^{12} \left (-x^7+10 x^6-44 x^5+120 x^4-240 x^3+352 x^2-320 x+128\right )}{e^{12} \left (x^7-10 x^6+40 x^5-80 x^4+80 x^3-32 x^2\right )} \, dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {\int -\frac {e^{12} \left (-x^7+10 x^6-44 x^5+120 x^4-240 x^3+352 x^2-320 x+128\right )-\exp \left (\frac {4 e^3 x-2 e^6 \left (x^3-7 x^2+4 x\right )-4 e^9 \left (x^4-5 x^3+4 x^2\right )+e^{12} \left (x^6-10 x^5+33 x^4-40 x^3+16 x^2\right )+1}{e^{12} \left (x^4-8 x^3+24 x^2-32 x+16\right )}\right ) \left (4 x+4 e^3 \left (3 x^2+2 x\right )-2 e^6 \left (x^4-8 x^3-16 x^2+8 x\right )-4 e^9 \left (3 x^4-22 x^3+16 x^2\right )-e^{12} \left (2 x^7-22 x^6+99 x^5-214 x^4+168 x^3+16 x^2-80 x+32\right )\right )}{-x^7+10 x^6-40 x^5+80 x^4-80 x^3+32 x^2}dx}{e^{12}}\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -\frac {\int \frac {e^{12} \left (-x^7+10 x^6-44 x^5+120 x^4-240 x^3+352 x^2-320 x+128\right )-\exp \left (\frac {4 e^3 x-2 e^6 \left (x^3-7 x^2+4 x\right )-4 e^9 \left (x^4-5 x^3+4 x^2\right )+e^{12} \left (x^6-10 x^5+33 x^4-40 x^3+16 x^2\right )+1}{e^{12} \left (x^4-8 x^3+24 x^2-32 x+16\right )}\right ) \left (4 x+4 e^3 \left (3 x^2+2 x\right )-2 e^6 \left (x^4-8 x^3-16 x^2+8 x\right )-4 e^9 \left (3 x^4-22 x^3+16 x^2\right )-e^{12} \left (2 x^7-22 x^6+99 x^5-214 x^4+168 x^3+16 x^2-80 x+32\right )\right )}{-x^7+10 x^6-40 x^5+80 x^4-80 x^3+32 x^2}dx}{e^{12}}\) |
| \(\Big \downarrow \) 2026 |
| \(\displaystyle -\frac {\int \frac {e^{12} \left (-x^7+10 x^6-44 x^5+120 x^4-240 x^3+352 x^2-320 x+128\right )-\exp \left (\frac {4 e^3 x-2 e^6 \left (x^3-7 x^2+4 x\right )-4 e^9 \left (x^4-5 x^3+4 x^2\right )+e^{12} \left (x^6-10 x^5+33 x^4-40 x^3+16 x^2\right )+1}{e^{12} \left (x^4-8 x^3+24 x^2-32 x+16\right )}\right ) \left (4 x+4 e^3 \left (3 x^2+2 x\right )-2 e^6 \left (x^4-8 x^3-16 x^2+8 x\right )-4 e^9 \left (3 x^4-22 x^3+16 x^2\right )-e^{12} \left (2 x^7-22 x^6+99 x^5-214 x^4+168 x^3+16 x^2-80 x+32\right )\right )}{x^2 \left (-x^5+10 x^4-40 x^3+80 x^2-80 x+32\right )}dx}{e^{12}}\) |
| \(\Big \downarrow \) 2007 |
| \(\displaystyle -\frac {\int \frac {e^{12} \left (-x^7+10 x^6-44 x^5+120 x^4-240 x^3+352 x^2-320 x+128\right )-\exp \left (\frac {4 e^3 x-2 e^6 \left (x^3-7 x^2+4 x\right )-4 e^9 \left (x^4-5 x^3+4 x^2\right )+e^{12} \left (x^6-10 x^5+33 x^4-40 x^3+16 x^2\right )+1}{e^{12} \left (x^4-8 x^3+24 x^2-32 x+16\right )}\right ) \left (4 x+4 e^3 \left (3 x^2+2 x\right )-2 e^6 \left (x^4-8 x^3-16 x^2+8 x\right )-4 e^9 \left (3 x^4-22 x^3+16 x^2\right )-e^{12} \left (2 x^7-22 x^6+99 x^5-214 x^4+168 x^3+16 x^2-80 x+32\right )\right )}{(2-x)^5 x^2}dx}{e^{12}}\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -\frac {\int \frac {\exp \left (\frac {\left (-e^6 \left (x^2-5 x+4\right ) x+2 e^3 x+1\right )^2}{e^{12} (x-2)^4}\right ) \left (4 e^9 \left (3 x^2-22 x+16\right ) x^2-4 e^3 (3 x+2) x+2 e^6 \left (x^3-8 x^2-16 x+8\right ) x-4 x+e^{12} \left (2 x^7-22 x^6+99 x^5-214 x^4+168 x^3+16 x^2-80 x+32\right )\right )-e^{12} (x-2)^5 \left (x^2+4\right )}{(2-x)^5 x^2}dx}{e^{12}}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {\int \left (\frac {e^{12} \left (x^2+4\right )}{x^2}+\frac {\exp \left (\frac {\left (-e^6 x^3+5 e^6 x^2+2 e^3 \left (1-2 e^3\right ) x+1\right )^2}{e^{12} (x-2)^4}\right ) \left (2 e^{12} x^7-22 e^{12} x^6+99 e^{12} x^5+2 e^6 \left (1+6 e^3-107 e^6\right ) x^4-16 e^6 \left (1-\frac {1}{2} e^3 \left (-11+21 e^3\right )\right ) x^3-12 e^3 \left (1-\frac {4}{3} e^3 \left (-2+4 e^3+e^6\right )\right ) x^2-4 \left (1+2 e^3 \left (1-2 e^3+10 e^9\right )\right ) x+32 e^{12}\right )}{(2-x)^5 x^2}\right )dx}{e^{12}}\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -\frac {-2 \int \exp \left (\frac {\left (-e^6 x^3+5 e^6 x^2+2 e^3 \left (1-2 e^3\right ) x+1\right )^2}{e^{12} (x-2)^4}+12\right )dx+2 \left (1+2 e^3\right )^4 \int \frac {\exp \left (\frac {\left (-e^6 x^3+5 e^6 x^2+2 e^3 \left (1-2 e^3\right ) x+1\right )^2}{e^{12} (x-2)^4}\right )}{(x-2)^5}dx-\left (1-4 e^3\right ) \left (1+2 e^3\right )^3 \int \frac {\exp \left (\frac {\left (-e^6 x^3+5 e^6 x^2+2 e^3 \left (1-2 e^3\right ) x+1\right )^2}{e^{12} (x-2)^4}\right )}{(x-2)^4}dx+\frac {1}{2} \left (1+2 e^3\right )^2 \left (1-2 e^3-4 e^6\right ) \int \frac {\exp \left (\frac {\left (-e^6 x^3+5 e^6 x^2+2 e^3 \left (1-2 e^3\right ) x+1\right )^2}{e^{12} (x-2)^4}\right )}{(x-2)^3}dx-\frac {1}{4} \left (1+2 e^3-4 e^6+16 e^{12}\right ) \int \frac {\exp \left (\frac {\left (-e^6 x^3+5 e^6 x^2+2 e^3 \left (1-2 e^3\right ) x+1\right )^2}{e^{12} (x-2)^4}\right )}{(x-2)^2}dx+\frac {1}{8} \left (1+2 e^3-4 e^6+16 e^{12}\right ) \int \frac {\exp \left (\frac {\left (-e^6 x^3+5 e^6 x^2+2 e^3 \left (1-2 e^3\right ) x+1\right )^2}{e^{12} (x-2)^4}\right )}{x-2}dx+\int \frac {\exp \left (\frac {\left (-e^6 x^3+5 e^6 x^2+2 e^3 \left (1-2 e^3\right ) x+1\right )^2}{e^{12} (x-2)^4}+12\right )}{x^2}dx-\frac {1}{8} \left (1+2 e^3-4 e^6\right ) \int \frac {\exp \left (\frac {\left (-e^6 x^3+5 e^6 x^2+2 e^3 \left (1-2 e^3\right ) x+1\right )^2}{e^{12} (x-2)^4}\right )}{x}dx+e^{12} x-\frac {4 e^{12}}{x}}{e^{12}}\) |
Input:
Int[(E^12*(128 - 320*x + 352*x^2 - 240*x^3 + 120*x^4 - 44*x^5 + 10*x^6 - x ^7) + E^((1 + 4*E^3*x + E^6*(-8*x + 14*x^2 - 2*x^3) + E^9*(-16*x^2 + 20*x^ 3 - 4*x^4) + E^12*(16*x^2 - 40*x^3 + 33*x^4 - 10*x^5 + x^6))/(E^12*(16 - 3 2*x + 24*x^2 - 8*x^3 + x^4)))*(-4*x + E^3*(-8*x - 12*x^2) + E^6*(16*x - 32 *x^2 - 16*x^3 + 2*x^4) + E^9*(64*x^2 - 88*x^3 + 12*x^4) + E^12*(32 - 80*x + 16*x^2 + 168*x^3 - 214*x^4 + 99*x^5 - 22*x^6 + 2*x^7)))/(E^12*(-32*x^2 + 80*x^3 - 80*x^4 + 40*x^5 - 10*x^6 + x^7)),x]
Output:
$Aborted
Timed out.
\[\int \frac {\left (\left (\left (2 x^{7}-22 x^{6}+99 x^{5}-214 x^{4}+168 x^{3}+16 x^{2}-80 x +32\right ) {\mathrm e}^{12}+\left (12 x^{4}-88 x^{3}+64 x^{2}\right ) {\mathrm e}^{9}+\left (2 x^{4}-16 x^{3}-32 x^{2}+16 x \right ) {\mathrm e}^{6}+\left (-12 x^{2}-8 x \right ) {\mathrm e}^{3}-4 x \right ) {\mathrm e}^{\frac {\left (\left (x^{6}-10 x^{5}+33 x^{4}-40 x^{3}+16 x^{2}\right ) {\mathrm e}^{12}+\left (-4 x^{4}+20 x^{3}-16 x^{2}\right ) {\mathrm e}^{9}+\left (-2 x^{3}+14 x^{2}-8 x \right ) {\mathrm e}^{6}+4 x \,{\mathrm e}^{3}+1\right ) {\mathrm e}^{-12}}{x^{4}-8 x^{3}+24 x^{2}-32 x +16}}+\left (-x^{7}+10 x^{6}-44 x^{5}+120 x^{4}-240 x^{3}+352 x^{2}-320 x +128\right ) {\mathrm e}^{12}\right ) {\mathrm e}^{-12}}{x^{7}-10 x^{6}+40 x^{5}-80 x^{4}+80 x^{3}-32 x^{2}}d x\]
Input:
int((((2*x^7-22*x^6+99*x^5-214*x^4+168*x^3+16*x^2-80*x+32)*exp(3)^4+(12*x^ 4-88*x^3+64*x^2)*exp(3)^3+(2*x^4-16*x^3-32*x^2+16*x)*exp(3)^2+(-12*x^2-8*x )*exp(3)-4*x)*exp(((x^6-10*x^5+33*x^4-40*x^3+16*x^2)*exp(3)^4+(-4*x^4+20*x ^3-16*x^2)*exp(3)^3+(-2*x^3+14*x^2-8*x)*exp(3)^2+4*x*exp(3)+1)/(x^4-8*x^3+ 24*x^2-32*x+16)/exp(3)^4)+(-x^7+10*x^6-44*x^5+120*x^4-240*x^3+352*x^2-320* x+128)*exp(3)^4)/(x^7-10*x^6+40*x^5-80*x^4+80*x^3-32*x^2)/exp(3)^4,x)
Output:
int((((2*x^7-22*x^6+99*x^5-214*x^4+168*x^3+16*x^2-80*x+32)*exp(3)^4+(12*x^ 4-88*x^3+64*x^2)*exp(3)^3+(2*x^4-16*x^3-32*x^2+16*x)*exp(3)^2+(-12*x^2-8*x )*exp(3)-4*x)*exp(((x^6-10*x^5+33*x^4-40*x^3+16*x^2)*exp(3)^4+(-4*x^4+20*x ^3-16*x^2)*exp(3)^3+(-2*x^3+14*x^2-8*x)*exp(3)^2+4*x*exp(3)+1)/(x^4-8*x^3+ 24*x^2-32*x+16)/exp(3)^4)+(-x^7+10*x^6-44*x^5+120*x^4-240*x^3+352*x^2-320* x+128)*exp(3)^4)/(x^7-10*x^6+40*x^5-80*x^4+80*x^3-32*x^2)/exp(3)^4,x)
Leaf count of result is larger than twice the leaf count of optimal. 104 vs. \(2 (33) = 66\).
Time = 0.11 (sec) , antiderivative size = 104, normalized size of antiderivative = 3.06 \[ \int \frac {e^{12} \left (128-320 x+352 x^2-240 x^3+120 x^4-44 x^5+10 x^6-x^7\right )+e^{\frac {1+4 e^3 x+e^6 \left (-8 x+14 x^2-2 x^3\right )+e^9 \left (-16 x^2+20 x^3-4 x^4\right )+e^{12} \left (16 x^2-40 x^3+33 x^4-10 x^5+x^6\right )}{e^{12} \left (16-32 x+24 x^2-8 x^3+x^4\right )}} \left (-4 x+e^3 \left (-8 x-12 x^2\right )+e^6 \left (16 x-32 x^2-16 x^3+2 x^4\right )+e^9 \left (64 x^2-88 x^3+12 x^4\right )+e^{12} \left (32-80 x+16 x^2+168 x^3-214 x^4+99 x^5-22 x^6+2 x^7\right )\right )}{e^{12} \left (-32 x^2+80 x^3-80 x^4+40 x^5-10 x^6+x^7\right )} \, dx=-\frac {x^{2} - e^{\left (\frac {{\left ({\left (x^{6} - 10 \, x^{5} + 33 \, x^{4} - 40 \, x^{3} + 16 \, x^{2}\right )} e^{12} - 4 \, {\left (x^{4} - 5 \, x^{3} + 4 \, x^{2}\right )} e^{9} - 2 \, {\left (x^{3} - 7 \, x^{2} + 4 \, x\right )} e^{6} + 4 \, x e^{3} + 1\right )} e^{\left (-12\right )}}{x^{4} - 8 \, x^{3} + 24 \, x^{2} - 32 \, x + 16}\right )} - 4}{x} \] Input:
integrate((((2*x^7-22*x^6+99*x^5-214*x^4+168*x^3+16*x^2-80*x+32)*exp(3)^4+ (12*x^4-88*x^3+64*x^2)*exp(3)^3+(2*x^4-16*x^3-32*x^2+16*x)*exp(3)^2+(-12*x ^2-8*x)*exp(3)-4*x)*exp(((x^6-10*x^5+33*x^4-40*x^3+16*x^2)*exp(3)^4+(-4*x^ 4+20*x^3-16*x^2)*exp(3)^3+(-2*x^3+14*x^2-8*x)*exp(3)^2+4*x*exp(3)+1)/(x^4- 8*x^3+24*x^2-32*x+16)/exp(3)^4)+(-x^7+10*x^6-44*x^5+120*x^4-240*x^3+352*x^ 2-320*x+128)*exp(3)^4)/(x^7-10*x^6+40*x^5-80*x^4+80*x^3-32*x^2)/exp(3)^4,x , algorithm="fricas")
Output:
-(x^2 - e^(((x^6 - 10*x^5 + 33*x^4 - 40*x^3 + 16*x^2)*e^12 - 4*(x^4 - 5*x^ 3 + 4*x^2)*e^9 - 2*(x^3 - 7*x^2 + 4*x)*e^6 + 4*x*e^3 + 1)*e^(-12)/(x^4 - 8 *x^3 + 24*x^2 - 32*x + 16)) - 4)/x
Leaf count of result is larger than twice the leaf count of optimal. 100 vs. \(2 (27) = 54\).
Time = 0.53 (sec) , antiderivative size = 100, normalized size of antiderivative = 2.94 \[ \int \frac {e^{12} \left (128-320 x+352 x^2-240 x^3+120 x^4-44 x^5+10 x^6-x^7\right )+e^{\frac {1+4 e^3 x+e^6 \left (-8 x+14 x^2-2 x^3\right )+e^9 \left (-16 x^2+20 x^3-4 x^4\right )+e^{12} \left (16 x^2-40 x^3+33 x^4-10 x^5+x^6\right )}{e^{12} \left (16-32 x+24 x^2-8 x^3+x^4\right )}} \left (-4 x+e^3 \left (-8 x-12 x^2\right )+e^6 \left (16 x-32 x^2-16 x^3+2 x^4\right )+e^9 \left (64 x^2-88 x^3+12 x^4\right )+e^{12} \left (32-80 x+16 x^2+168 x^3-214 x^4+99 x^5-22 x^6+2 x^7\right )\right )}{e^{12} \left (-32 x^2+80 x^3-80 x^4+40 x^5-10 x^6+x^7\right )} \, dx=- x + \frac {e^{\frac {4 x e^{3} + \left (- 2 x^{3} + 14 x^{2} - 8 x\right ) e^{6} + \left (- 4 x^{4} + 20 x^{3} - 16 x^{2}\right ) e^{9} + \left (x^{6} - 10 x^{5} + 33 x^{4} - 40 x^{3} + 16 x^{2}\right ) e^{12} + 1}{\left (x^{4} - 8 x^{3} + 24 x^{2} - 32 x + 16\right ) e^{12}}}}{x} + \frac {4}{x} \] Input:
integrate((((2*x**7-22*x**6+99*x**5-214*x**4+168*x**3+16*x**2-80*x+32)*exp (3)**4+(12*x**4-88*x**3+64*x**2)*exp(3)**3+(2*x**4-16*x**3-32*x**2+16*x)*e xp(3)**2+(-12*x**2-8*x)*exp(3)-4*x)*exp(((x**6-10*x**5+33*x**4-40*x**3+16* x**2)*exp(3)**4+(-4*x**4+20*x**3-16*x**2)*exp(3)**3+(-2*x**3+14*x**2-8*x)* exp(3)**2+4*x*exp(3)+1)/(x**4-8*x**3+24*x**2-32*x+16)/exp(3)**4)+(-x**7+10 *x**6-44*x**5+120*x**4-240*x**3+352*x**2-320*x+128)*exp(3)**4)/(x**7-10*x* *6+40*x**5-80*x**4+80*x**3-32*x**2)/exp(3)**4,x)
Output:
-x + exp((4*x*exp(3) + (-2*x**3 + 14*x**2 - 8*x)*exp(6) + (-4*x**4 + 20*x* *3 - 16*x**2)*exp(9) + (x**6 - 10*x**5 + 33*x**4 - 40*x**3 + 16*x**2)*exp( 12) + 1)*exp(-12)/(x**4 - 8*x**3 + 24*x**2 - 32*x + 16))/x + 4/x
Leaf count of result is larger than twice the leaf count of optimal. 697 vs. \(2 (33) = 66\).
Time = 1.25 (sec) , antiderivative size = 697, normalized size of antiderivative = 20.50 \[ \int \frac {e^{12} \left (128-320 x+352 x^2-240 x^3+120 x^4-44 x^5+10 x^6-x^7\right )+e^{\frac {1+4 e^3 x+e^6 \left (-8 x+14 x^2-2 x^3\right )+e^9 \left (-16 x^2+20 x^3-4 x^4\right )+e^{12} \left (16 x^2-40 x^3+33 x^4-10 x^5+x^6\right )}{e^{12} \left (16-32 x+24 x^2-8 x^3+x^4\right )}} \left (-4 x+e^3 \left (-8 x-12 x^2\right )+e^6 \left (16 x-32 x^2-16 x^3+2 x^4\right )+e^9 \left (64 x^2-88 x^3+12 x^4\right )+e^{12} \left (32-80 x+16 x^2+168 x^3-214 x^4+99 x^5-22 x^6+2 x^7\right )\right )}{e^{12} \left (-32 x^2+80 x^3-80 x^4+40 x^5-10 x^6+x^7\right )} \, dx =\text {Too large to display} \] Input:
integrate((((2*x^7-22*x^6+99*x^5-214*x^4+168*x^3+16*x^2-80*x+32)*exp(3)^4+ (12*x^4-88*x^3+64*x^2)*exp(3)^3+(2*x^4-16*x^3-32*x^2+16*x)*exp(3)^2+(-12*x ^2-8*x)*exp(3)-4*x)*exp(((x^6-10*x^5+33*x^4-40*x^3+16*x^2)*exp(3)^4+(-4*x^ 4+20*x^3-16*x^2)*exp(3)^3+(-2*x^3+14*x^2-8*x)*exp(3)^2+4*x*exp(3)+1)/(x^4- 8*x^3+24*x^2-32*x+16)/exp(3)^4)+(-x^7+10*x^6-44*x^5+120*x^4-240*x^3+352*x^ 2-320*x+128)*exp(3)^4)/(x^7-10*x^6+40*x^5-80*x^4+80*x^3-32*x^2)/exp(3)^4,x , algorithm="maxima")
Output:
-1/3*((3*x - 8*(15*x^3 - 75*x^2 + 130*x - 77)/(x^4 - 8*x^3 + 24*x^2 - 32*x + 16) + 30*log(x - 2))*e^12 - 2*(2*(15*x^4 - 105*x^3 + 260*x^2 - 250*x + 48)/(x^5 - 8*x^4 + 24*x^3 - 32*x^2 + 16*x) + 15*log(x - 2) - 15*log(x))*e^ 12 + 10*(4*(6*x^3 - 27*x^2 + 44*x - 25)/(x^4 - 8*x^3 + 24*x^2 - 32*x + 16) - 3*log(x - 2))*e^12 + 10*(2*(3*x^3 - 21*x^2 + 52*x - 50)/(x^4 - 8*x^3 + 24*x^2 - 32*x + 16) + 3*log(x - 2) - 3*log(x))*e^12 - 132*(x^3 - 3*x^2 + 4 *x - 2)*e^12/(x^4 - 8*x^3 + 24*x^2 - 32*x + 16) + 60*(3*x^2 - 4*x + 2)*e^1 2/(x^4 - 8*x^3 + 24*x^2 - 32*x + 16) - 120*(2*x - 1)*e^12/(x^4 - 8*x^3 + 2 4*x^2 - 32*x + 16) + 264*e^12/(x^4 - 8*x^3 + 24*x^2 - 32*x + 16) - 3*e^(x^ 2 - 2*x + 1/(x^4*e^12 - 8*x^3*e^12 + 24*x^2*e^12 - 32*x*e^12 + 16*e^12) + 8/(x^4*e^9 - 8*x^3*e^9 + 24*x^2*e^9 - 32*x*e^9 + 16*e^9) + 24/(x^4*e^6 - 8 *x^3*e^6 + 24*x^2*e^6 - 32*x*e^6 + 16*e^6) + 32/(x^4*e^3 - 8*x^3*e^3 + 24* x^2*e^3 - 32*x*e^3 + 16*e^3) + 16/(x^4 - 8*x^3 + 24*x^2 - 32*x + 16) + 4/( x^3*e^9 - 6*x^2*e^9 + 12*x*e^9 - 8*e^9) + 24/(x^3*e^6 - 6*x^2*e^6 + 12*x*e ^6 - 8*e^6) + 48/(x^3*e^3 - 6*x^2*e^3 + 12*x*e^3 - 8*e^3) + 32/(x^3 - 6*x^ 2 + 12*x - 8) + 2/(x^2*e^6 - 4*x*e^6 + 4*e^6) + 8/(x^2*e^3 - 4*x*e^3 + 4*e ^3) + 8/(x^2 - 4*x + 4) - 2/(x*e^6 - 2*e^6) - 12/(x*e^3 - 2*e^3) - 16/(x - 2) - 4*e^(-3) + 5)/x)*e^(-12)
Leaf count of result is larger than twice the leaf count of optimal. 160 vs. \(2 (33) = 66\).
Time = 2.12 (sec) , antiderivative size = 160, normalized size of antiderivative = 4.71 \[ \int \frac {e^{12} \left (128-320 x+352 x^2-240 x^3+120 x^4-44 x^5+10 x^6-x^7\right )+e^{\frac {1+4 e^3 x+e^6 \left (-8 x+14 x^2-2 x^3\right )+e^9 \left (-16 x^2+20 x^3-4 x^4\right )+e^{12} \left (16 x^2-40 x^3+33 x^4-10 x^5+x^6\right )}{e^{12} \left (16-32 x+24 x^2-8 x^3+x^4\right )}} \left (-4 x+e^3 \left (-8 x-12 x^2\right )+e^6 \left (16 x-32 x^2-16 x^3+2 x^4\right )+e^9 \left (64 x^2-88 x^3+12 x^4\right )+e^{12} \left (32-80 x+16 x^2+168 x^3-214 x^4+99 x^5-22 x^6+2 x^7\right )\right )}{e^{12} \left (-32 x^2+80 x^3-80 x^4+40 x^5-10 x^6+x^7\right )} \, dx=-\frac {{\left (x^{2} e^{12} - 4 \, e^{12} - e^{\left (\frac {16 \, x^{6} e^{12} - 160 \, x^{5} e^{12} + 528 \, x^{4} e^{12} - 64 \, x^{4} e^{9} - x^{4} - 640 \, x^{3} e^{12} + 320 \, x^{3} e^{9} - 32 \, x^{3} e^{6} + 8 \, x^{3} + 256 \, x^{2} e^{12} - 256 \, x^{2} e^{9} + 224 \, x^{2} e^{6} - 24 \, x^{2} - 128 \, x e^{6} + 64 \, x e^{3} + 32 \, x}{16 \, {\left (x^{4} e^{12} - 8 \, x^{3} e^{12} + 24 \, x^{2} e^{12} - 32 \, x e^{12} + 16 \, e^{12}\right )}} + \frac {1}{16} \, e^{\left (-12\right )} + 12\right )}\right )} e^{\left (-12\right )}}{x} \] Input:
integrate((((2*x^7-22*x^6+99*x^5-214*x^4+168*x^3+16*x^2-80*x+32)*exp(3)^4+ (12*x^4-88*x^3+64*x^2)*exp(3)^3+(2*x^4-16*x^3-32*x^2+16*x)*exp(3)^2+(-12*x ^2-8*x)*exp(3)-4*x)*exp(((x^6-10*x^5+33*x^4-40*x^3+16*x^2)*exp(3)^4+(-4*x^ 4+20*x^3-16*x^2)*exp(3)^3+(-2*x^3+14*x^2-8*x)*exp(3)^2+4*x*exp(3)+1)/(x^4- 8*x^3+24*x^2-32*x+16)/exp(3)^4)+(-x^7+10*x^6-44*x^5+120*x^4-240*x^3+352*x^ 2-320*x+128)*exp(3)^4)/(x^7-10*x^6+40*x^5-80*x^4+80*x^3-32*x^2)/exp(3)^4,x , algorithm="giac")
Output:
-(x^2*e^12 - 4*e^12 - e^(1/16*(16*x^6*e^12 - 160*x^5*e^12 + 528*x^4*e^12 - 64*x^4*e^9 - x^4 - 640*x^3*e^12 + 320*x^3*e^9 - 32*x^3*e^6 + 8*x^3 + 256* x^2*e^12 - 256*x^2*e^9 + 224*x^2*e^6 - 24*x^2 - 128*x*e^6 + 64*x*e^3 + 32* x)/(x^4*e^12 - 8*x^3*e^12 + 24*x^2*e^12 - 32*x*e^12 + 16*e^12) + 1/16*e^(- 12) + 12))*e^(-12)/x
Time = 5.45 (sec) , antiderivative size = 358, normalized size of antiderivative = 10.53 \[ \int \frac {e^{12} \left (128-320 x+352 x^2-240 x^3+120 x^4-44 x^5+10 x^6-x^7\right )+e^{\frac {1+4 e^3 x+e^6 \left (-8 x+14 x^2-2 x^3\right )+e^9 \left (-16 x^2+20 x^3-4 x^4\right )+e^{12} \left (16 x^2-40 x^3+33 x^4-10 x^5+x^6\right )}{e^{12} \left (16-32 x+24 x^2-8 x^3+x^4\right )}} \left (-4 x+e^3 \left (-8 x-12 x^2\right )+e^6 \left (16 x-32 x^2-16 x^3+2 x^4\right )+e^9 \left (64 x^2-88 x^3+12 x^4\right )+e^{12} \left (32-80 x+16 x^2+168 x^3-214 x^4+99 x^5-22 x^6+2 x^7\right )\right )}{e^{12} \left (-32 x^2+80 x^3-80 x^4+40 x^5-10 x^6+x^7\right )} \, dx=\frac {4}{x}-x+\frac {{\mathrm {e}}^{\frac {{\mathrm {e}}^{-12}}{x^4-8\,x^3+24\,x^2-32\,x+16}}\,{\mathrm {e}}^{\frac {x^6}{x^4-8\,x^3+24\,x^2-32\,x+16}}\,{\mathrm {e}}^{-\frac {10\,x^5}{x^4-8\,x^3+24\,x^2-32\,x+16}}\,{\mathrm {e}}^{\frac {16\,x^2}{x^4-8\,x^3+24\,x^2-32\,x+16}}\,{\mathrm {e}}^{\frac {33\,x^4}{x^4-8\,x^3+24\,x^2-32\,x+16}}\,{\mathrm {e}}^{-\frac {40\,x^3}{x^4-8\,x^3+24\,x^2-32\,x+16}}\,{\mathrm {e}}^{\frac {4\,x\,{\mathrm {e}}^{-9}}{x^4-8\,x^3+24\,x^2-32\,x+16}}\,{\mathrm {e}}^{-\frac {8\,x\,{\mathrm {e}}^{-6}}{x^4-8\,x^3+24\,x^2-32\,x+16}}\,{\mathrm {e}}^{-\frac {2\,x^3\,{\mathrm {e}}^{-6}}{x^4-8\,x^3+24\,x^2-32\,x+16}}\,{\mathrm {e}}^{-\frac {4\,x^4\,{\mathrm {e}}^{-3}}{x^4-8\,x^3+24\,x^2-32\,x+16}}\,{\mathrm {e}}^{-\frac {16\,x^2\,{\mathrm {e}}^{-3}}{x^4-8\,x^3+24\,x^2-32\,x+16}}\,{\mathrm {e}}^{\frac {14\,x^2\,{\mathrm {e}}^{-6}}{x^4-8\,x^3+24\,x^2-32\,x+16}}\,{\mathrm {e}}^{\frac {20\,x^3\,{\mathrm {e}}^{-3}}{x^4-8\,x^3+24\,x^2-32\,x+16}}}{x} \] Input:
int(-(exp(-12)*(exp((exp(-12)*(4*x*exp(3) - exp(6)*(8*x - 14*x^2 + 2*x^3) - exp(9)*(16*x^2 - 20*x^3 + 4*x^4) + exp(12)*(16*x^2 - 40*x^3 + 33*x^4 - 1 0*x^5 + x^6) + 1))/(24*x^2 - 32*x - 8*x^3 + x^4 + 16))*(exp(12)*(16*x^2 - 80*x + 168*x^3 - 214*x^4 + 99*x^5 - 22*x^6 + 2*x^7 + 32) - exp(3)*(8*x + 1 2*x^2) - 4*x + exp(6)*(16*x - 32*x^2 - 16*x^3 + 2*x^4) + exp(9)*(64*x^2 - 88*x^3 + 12*x^4)) - exp(12)*(320*x - 352*x^2 + 240*x^3 - 120*x^4 + 44*x^5 - 10*x^6 + x^7 - 128)))/(32*x^2 - 80*x^3 + 80*x^4 - 40*x^5 + 10*x^6 - x^7) ,x)
Output:
4/x - x + (exp(exp(-12)/(24*x^2 - 32*x - 8*x^3 + x^4 + 16))*exp(x^6/(24*x^ 2 - 32*x - 8*x^3 + x^4 + 16))*exp(-(10*x^5)/(24*x^2 - 32*x - 8*x^3 + x^4 + 16))*exp((16*x^2)/(24*x^2 - 32*x - 8*x^3 + x^4 + 16))*exp((33*x^4)/(24*x^ 2 - 32*x - 8*x^3 + x^4 + 16))*exp(-(40*x^3)/(24*x^2 - 32*x - 8*x^3 + x^4 + 16))*exp((4*x*exp(-9))/(24*x^2 - 32*x - 8*x^3 + x^4 + 16))*exp(-(8*x*exp( -6))/(24*x^2 - 32*x - 8*x^3 + x^4 + 16))*exp(-(2*x^3*exp(-6))/(24*x^2 - 32 *x - 8*x^3 + x^4 + 16))*exp(-(4*x^4*exp(-3))/(24*x^2 - 32*x - 8*x^3 + x^4 + 16))*exp(-(16*x^2*exp(-3))/(24*x^2 - 32*x - 8*x^3 + x^4 + 16))*exp((14*x ^2*exp(-6))/(24*x^2 - 32*x - 8*x^3 + x^4 + 16))*exp((20*x^3*exp(-3))/(24*x ^2 - 32*x - 8*x^3 + x^4 + 16)))/x
Time = 0.77 (sec) , antiderivative size = 440, normalized size of antiderivative = 12.94 \[ \int \frac {e^{12} \left (128-320 x+352 x^2-240 x^3+120 x^4-44 x^5+10 x^6-x^7\right )+e^{\frac {1+4 e^3 x+e^6 \left (-8 x+14 x^2-2 x^3\right )+e^9 \left (-16 x^2+20 x^3-4 x^4\right )+e^{12} \left (16 x^2-40 x^3+33 x^4-10 x^5+x^6\right )}{e^{12} \left (16-32 x+24 x^2-8 x^3+x^4\right )}} \left (-4 x+e^3 \left (-8 x-12 x^2\right )+e^6 \left (16 x-32 x^2-16 x^3+2 x^4\right )+e^9 \left (64 x^2-88 x^3+12 x^4\right )+e^{12} \left (32-80 x+16 x^2+168 x^3-214 x^4+99 x^5-22 x^6+2 x^7\right )\right )}{e^{12} \left (-32 x^2+80 x^3-80 x^4+40 x^5-10 x^6+x^7\right )} \, dx=\frac {e^{\frac {e^{12} x^{6}-8 e^{12} x^{5}+24 e^{12} x^{4}-32 e^{12} x^{3}+120 e^{12} x^{2}+112 e^{12}+20 e^{9} x^{3}+14 e^{6} x^{2}+4 e^{3} x +1}{e^{12} x^{4}-8 e^{12} x^{3}+24 e^{12} x^{2}-32 e^{12} x +16 e^{12}}}-e^{\frac {2 e^{6} x^{5}-16 e^{6} x^{4}+64 e^{6} x^{3}-64 e^{6} x^{2}+224 e^{6} x +4 e^{3} x^{4}+16 e^{3} x^{2}+2 x^{3}+8 x}{e^{6} x^{4}-8 e^{6} x^{3}+24 e^{6} x^{2}-32 e^{6} x +16 e^{6}}} e^{7} x^{2}+4 e^{\frac {2 e^{6} x^{5}-16 e^{6} x^{4}+64 e^{6} x^{3}-64 e^{6} x^{2}+224 e^{6} x +4 e^{3} x^{4}+16 e^{3} x^{2}+2 x^{3}+8 x}{e^{6} x^{4}-8 e^{6} x^{3}+24 e^{6} x^{2}-32 e^{6} x +16 e^{6}}} e^{7}}{e^{\frac {2 e^{6} x^{5}-16 e^{6} x^{4}+64 e^{6} x^{3}-64 e^{6} x^{2}+224 e^{6} x +4 e^{3} x^{4}+16 e^{3} x^{2}+2 x^{3}+8 x}{e^{6} x^{4}-8 e^{6} x^{3}+24 e^{6} x^{2}-32 e^{6} x +16 e^{6}}} e^{7} x} \] Input:
int((((2*x^7-22*x^6+99*x^5-214*x^4+168*x^3+16*x^2-80*x+32)*exp(3)^4+(12*x^ 4-88*x^3+64*x^2)*exp(3)^3+(2*x^4-16*x^3-32*x^2+16*x)*exp(3)^2+(-12*x^2-8*x )*exp(3)-4*x)*exp(((x^6-10*x^5+33*x^4-40*x^3+16*x^2)*exp(3)^4+(-4*x^4+20*x ^3-16*x^2)*exp(3)^3+(-2*x^3+14*x^2-8*x)*exp(3)^2+4*x*exp(3)+1)/(x^4-8*x^3+ 24*x^2-32*x+16)/exp(3)^4)+(-x^7+10*x^6-44*x^5+120*x^4-240*x^3+352*x^2-320* x+128)*exp(3)^4)/(x^7-10*x^6+40*x^5-80*x^4+80*x^3-32*x^2)/exp(3)^4,x)
Output:
(e**((e**12*x**6 - 8*e**12*x**5 + 24*e**12*x**4 - 32*e**12*x**3 + 120*e**1 2*x**2 + 112*e**12 + 20*e**9*x**3 + 14*e**6*x**2 + 4*e**3*x + 1)/(e**12*x* *4 - 8*e**12*x**3 + 24*e**12*x**2 - 32*e**12*x + 16*e**12)) - e**((2*e**6* x**5 - 16*e**6*x**4 + 64*e**6*x**3 - 64*e**6*x**2 + 224*e**6*x + 4*e**3*x* *4 + 16*e**3*x**2 + 2*x**3 + 8*x)/(e**6*x**4 - 8*e**6*x**3 + 24*e**6*x**2 - 32*e**6*x + 16*e**6))*e**7*x**2 + 4*e**((2*e**6*x**5 - 16*e**6*x**4 + 64 *e**6*x**3 - 64*e**6*x**2 + 224*e**6*x + 4*e**3*x**4 + 16*e**3*x**2 + 2*x* *3 + 8*x)/(e**6*x**4 - 8*e**6*x**3 + 24*e**6*x**2 - 32*e**6*x + 16*e**6))* e**7)/(e**((2*e**6*x**5 - 16*e**6*x**4 + 64*e**6*x**3 - 64*e**6*x**2 + 224 *e**6*x + 4*e**3*x**4 + 16*e**3*x**2 + 2*x**3 + 8*x)/(e**6*x**4 - 8*e**6*x **3 + 24*e**6*x**2 - 32*e**6*x + 16*e**6))*e**7*x)